Conventionally, electric and magnetic fields follow what is termed as the right-hand rule: an electrical current flowing through a conductor results in a magnetic flux revolving around the conductor in a clockwise direction as observed from the direction of the source of the current. This is termed the right-hand rule because, while extending the thumb of one's right hand, the direction one's fingers curl indicates the direction in which induced magnetic flux revolves. However, as originally termed by V. G. Veselago, “left-handedness” can exist. In other words, a material can exist in which the flow of the electric current causes magnetic flux of an opposite sense, revolving in a counter-clockwise direction from the perspective of the source of the current.
More specifically, conventional, right-handed materials have positive values of electric permittivity, ∈, and magnetic permeability, μ. Therefore, as shown in FIG. 1, if ranges of electric permittivity and magnetic permeability are graphed in a two-dimensional Cartesian space 100, the properties of natural materials fall in a first, upper-right quadrant 110 of the graph 100. On the other hand, left-handed materials or meta-materials have negative values of both electric permittivity and magnetic permeability. As a result, these quantities describing left-handed materials fall in a third, lower-left quadrant 120 of the graph 100.
Left-handed materials can have useful properties in manipulating electromagnetic signals, for example, in refracting those signals. As shown in FIG. 2, an electromagnetic signal 200 passing from a first right-handed material 210 into a second right-handed material 220 at a boundary 230 will always be refracted toward the normal 240 of the boundary 230. This is because the index of refraction n for such signals derived from Snell's law is always a positive quantity. According to Snell's law, the index of refraction n can be derived from the equation n2=∈μ. Therefore, n=√{square root over (∈μ)}, conventionally, necessarily yields a positive quantity. Because n is a positive quantity, as is understood by one ordinarily skilled in the art, the electromagnetic signal 200 always is refracted toward the normal 240. However, as suggested by Veselago, if the electric permittivity ∈ and magnetic permeability μ are both negative numbers, then the square root of the combined quantity will yield a negative number. Thus, as shown in FIG. 3, because the index of refraction can be a negative quantity, a signal 300 passing from a right-handed material 310 into a left-handed material 320 at a boundary 330 is refracted away from the normal 340.
A material exhibiting such refractive properties, to name one example, would be useful in allowing different ways of focusing electromagnetic signal transmission and reception, such as in radar. Antennae or electromagnetic lenses incorporating left-handed materials for the transmission and reception of such signals could be shaped differently than devices constructed of only right-handed materials. However, left-handed materials are only theorized, and currently there are no methods for fabricating left-handed materials. Therefore, there is an unmet need in the art for a method to fabricate left-handed materials, as well as for the materials such a method can produce.